<h2>Problem 284</h2>
<div style="color:#666;font-size:80%;">27 March 2010</div><br />
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<p>The 3-digit number 376 in the decimal numbering system is an example of numbers with the special property that its square ends with the same digits: 376<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> = 141376. Let's call a number with this property a steady square.</p>

<p>Steady squares can also be observed in other numbering systems. In the base 14 numbering system, the 3-digit number c37 is also a steady square: c37<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /> = aa0c37, and the sum of its digits is c+3+7=18 in the same numbering system. The letters a, b, c and d are used for the 10, 11, 12 and 13 digits respectively, in a manner similar to the hexadecimal numbering system.</p>

<p>For 1 <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> n <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 9, the sum of the digits of all the n-digit steady squares in the base 14 numbering system is 2d8 (582 decimal). Steady squares with leading 0's are not allowed.</p>

<p>Find the sum of the digits of all the n-digit steady squares in the base 14 numbering system for<BR>
1 <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> n <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 10000 (decimal) and give your answer in the base 14 system using lower case letters where necessary.</p>
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